Anyonic quantum symmetries of finite spaces

Autor:	Anshu, Bhattacharjee, Suvrajit, Rahaman, Atibur, Roy, Sutanu
Rok vydání:	2022
Předmět:	Mathematics - Quantum Algebra Mathematics - Operator Algebras
Zdroj:	Lett. Math. Phys. 113 (2023), no. 6, 116
Druh dokumentu:	Working Paper
DOI:	10.1007/s11005-023-01736-1
Popis:	We construct a braided analogue of the quantum permutation group and show that it is the universal braided compact quantum group acting on a finite space in the category of $\mathbb{Z}/N\mathbb{Z}$-$\textrm{C}^*$-algebras with a twisted monoidal structure. As an application, we prove the existence of braided quantum symmetries of finite, simple, undirected, circulant graphs, explicitly compute it for several examples, and obtain a generalization of a result of Banica in this direction. Finally, in an appendix, we briefly describe the irreducible representations of this braided analogue of the quantum permutation group and their fusion rules. Comment: Revised version following the referee's suggestions. To appear in Letters in Mathematical Physics
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2207.08153 Zobrazit plný text záznamu Plný text ve formátu PDF Plný text ve formátu HTML
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